Halliday & Matthiessen (2014: 501-2):
An expression beginning the time ... may thus have three distinct functional values:
(1) as hypotactic enhancing clause ‘(on the occasion) when ... ’, e.g.||| [×β:] the time we first met || [α:] he hardly spoke to me at all |||
(2) as nominal group with elaborating embedded clause ‘the time which ... ’, e.g.||| the time [[ = (which) I like best ]] is the hour before dawn |||
(3) as nominal group with enhancing embedded clause ‘the time when ... ’, e.g.||| the time [[ × (when/that) you should leave ]] is when the lights go out |||
A hypotactic enhancing clause introduced by the time is agnate with other hypotactic temporal clauses and, by a further step, with paratactic temporal clauses: when we first met, he hardly ... ; we first met in June; then he hardly ... . The expression the time has come to serve as a structural conjunction; and the item time can thus no longer be modified in the way the Head noun of a nominal group can be (an example such as the early time we first met, he hardly spoke to me at all is impossible).* In contrast, the nominal groups in (2) and (3) can be expanded, since they have the full potential of nominal groups: the early time (which) I like best is the hour before dawn; the latest time (when/that) you should leave is when the lights go out. As illustrated by the examples, such enhanced nominal groups typically serve as participants in ‘relational’ clauses.
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* However, certain conjunctive features may be included in the nominal expression: the first time we met/the last time we met/the only time we met, he hardly spoke to me at all.